Q. 244.1( 52 Votes )

# Show that the rig

Answer :

Let r and h be the radius and height of the cone respectively.

Then, the volume (V) of the cone is given by:

V= The surface area (S) of the cone

S = πrl

=    Then,   Now, if So, when then > 0

Then, by second derivative test, the surface area of the cone is the least when .

So when then h = Therefore, for a given volume, the right circular cone of the least curved surface has an altitude equal to √2 times the radius of the base.

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